Problem 19 Find the slope and \(y\) -interc... [FREE SOLUTION] (2024)

Get started for free

Log In Start studying!

Get started for free Log out

Chapter 0: Problem 19

Find the slope and \(y\) -intercept. $$y-3 x=6$$

Short Answer

Expert verified

The slope is 3 and the y-intercept is 6.

Step by step solution


Solve for y

Add 3x to both sides of the equation to get y = 3x + 6. Now the equation is in slope-intercept form.


Identify the Slope

Compare the equation y = 3x + 6 to the general form y = mx + b. The coefficient of x is the slope, so m = 3.


Identify the y-intercept

Compare the equation y = 3x + 6 to the general form y = mx + b. The constant term is the y-intercept, so b = 6.

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

linear equations

In mathematics, linear equations are equations of first degree. This means the highest exponent of the variable (commonly \(x\)) is 1. A linear equation generally looks like \(ax + b = 0\). In geometry, linear equations represent straight-line graphs.
For example, in the given equation \(y - 3x = 6\), it is linear because both \(y\) and \(x\) are to the first power. Converting it into \(y = 3x + 6\) doesn't change its nature; it still represents a straight line. Linear equations have many applications in different fields, including physics, economics, and biology.


The slope, often denoted as \(m\), measures the steepness of a line. It is calculated as the 'rise' (the change in \(y\)) over the 'run' (the change in \(x\)). In the slope-intercept form of a linear equation, \(y = mx + b\), \(m\) is the slope.
For example, in the equation \(y = 3x + 6\), the coefficient of \(x\) is the slope. Therefore, the slope is \(m=3\). This means for every one unit increase in \(x\), \(y\) increases by 3 units. Knowing the slope helps in understanding how quickly or slowly the value of \(y\) changes with \(x\).


The \(y\)-intercept is where the line crosses the \(y\)-axis. In the slope-intercept form, \(y = mx + b\), \(b\) is the \(y\)-intercept.
For instance, in \(y = 3x + 6\), the constant term 6 is the \(y\)-intercept. This tells us that if \(x=0\), then \(y=6\). Therefore, the graph intersects the \(y\)-axis at the point (0, 6). The \(y\)-intercept is essential for graphing because it provides an initial point for drawing the line.

solving equations

Solving linear equations involves finding the values of variables that make the equation true. This often includes isolating the variable on one side of the equation.
For the equation \(y - 3x = 6\), adding \(3x\) to both sides rewrites it as \(y = 3x + 6\). This equation is now arranged in the slope-intercept form, making it easier to identify the slope and \(y\)-intercept.
Solving equations may involve other techniques like factoring or using the quadratic formula for different types of equations, but for linear equations, the steps are usually straightforward and involve basic algebraic operations.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Problem 19 Find the slope and \(y\) -interc... [FREE SOLUTION] (3)

Most popular questions from this chapter

Use the TABLE feature to construct a table for the function under the givenconditions.$$f(x)=\frac{3}{x^{2}-4} ; \text { TblStart }=-3 ; \Delta \mathrm{Tbl}=1$$Find the domain of each function given below. $$f(x)=\frac{2}{x+3}$$Find the domain of each function given below.\(g(x)=\frac{x-1}{x^{2}-36} \quad\) (Hint: Factor the denominator.)In computing the dosage for chemotherapy, a patient's body surface area isneeded. A good approximation of a person's surface area \(s,\) in square meters\(\left(m^{2}\right),\) is given by the formula$$s=\sqrt{\frac{h w}{3600}},$$where w is the patient's weight in kilograms (kg) and h is the patient'sheight in centimeters (cm). (Source: U.S. Oncology.) Use the preceding information. Round your answers to the nearest thousandth.Assume that a patient's weight is 70 kg. Approximate the patient's surfacearea assuming that: a) The patients height is 150 cm. b) The patients height is 180 cm.A large crane is being depreciated according to the model \(V(t)=900-60 t\)where \(V(t)\) is measured in thousands of dollars and \(t\) is the number ofyears since 2005 . If the crane is to be depreciated until its value is 0dollars, what is the domain of the depreciation model?
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation


Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Mechanics Maths

Read Explanation

Applied Mathematics

Read Explanation

Logic and Functions

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free

This website uses cookies to improve your experience. We'll assume you're ok with this, but you can opt-out if you wish. Accept

Privacy & Cookies Policy

Privacy Overview

This website uses cookies to improve your experience while you navigate through the website. Out of these, the cookies that are categorized as necessary are stored on your browser as they are essential for the working of basic functionalities of the website. We also use third-party cookies that help us analyze and understand how you use this website. These cookies will be stored in your browser only with your consent. You also have the option to opt-out of these cookies. But opting out of some of these cookies may affect your browsing experience.


Always Enabled

Necessary cookies are absolutely essential for the website to function properly. This category only includes cookies that ensures basic functionalities and security features of the website. These cookies do not store any personal information.


Any cookies that may not be particularly necessary for the website to function and is used specifically to collect user personal data via analytics, ads, other embedded contents are termed as non-necessary cookies. It is mandatory to procure user consent prior to running these cookies on your website.

Problem 19 Find the slope and \(y\) -interc... [FREE SOLUTION] (2024)


How do you find the slope and Y value? ›

The equation of the line is written in the slope-intercept form, which is: y = mx + b, where m represents the slope and b represents the y-intercept. In our equation, y = 6x + 2, we see that the slope of the line is 6.

How do you solve for y and state the slope and y-intercept? ›

Summary. The slope-intercept form of a line is: y=mx+b where m is the slope and b is the y-intercept. The y-intercept is always where the line intersects the y-axis, and will always appear as (0,b) in coordinate form.

How to calculate y-intercept? ›

Since the y-intercept always has a corresponding x-value of 0, replace x with 0 in the equation and solve for y. On a graph, the y-intercept can be found by finding the value of y when x=0.

What is the Y formula for slope? ›

y = mx + b is the slope-intercept form of the equation of a straight line. In the equation y = mx + b, m is the slope of the line and b is the intercept. x and y represent the distance of the line from the x-axis and y-axis, respectively. The value of b is equal to y when x = 0, and m shows how steep the line is.

How to find slope and y-intercept with two points? ›

Given two points on a line, we can write an equation for that line by finding the slope between those points, then solving for the y-intercept in the slope-intercept equation y=mx+b.

What is the slope of =- 12? ›

Using the slope-intercept form, the slope is 0 .

How to find the value of y? ›

To find a value for y given a value for x, substitute the x-value into the expression. Consider the equation y = 2x + 6. Find the value for y when x = 5: Substitute the value for x into the equation.

What is the slope of y? ›

In an equation in slope-intercept form (y=mx+b) the slope is m and the y-intercept is b. We can also rewrite certain equations to look more like slope-intercept form. For example, y=x can be rewritten as y=1x+0, so its slope is 1 and its y-intercept is 0.

How to graph slope and y-intercept? ›

To graph a linear equation in slope-intercept form, we can use the information given by that form. For example, y=2x+3 tells us that the slope of the line is 2 and the y-intercept is at (0,3). This gives us one point the line goes through, and the direction we should continue from that point to draw the entire line.

How to find slope and y-intercept from standard form? ›

Or we can convert the standard form equation to the slope intercept equation y=mx+ b; using this equation, the value m=slope and b=y intercept.

What is the formula for the slope intercept? ›

The slope intercept form in math is one of the forms used to calculate the equation of a straight line, given the slope of the line and intercept it forms with the y-axis. The slope intercept form is given as, y = mx + b, where 'm' is the slope of the straight line and 'b' is the y-intercept.

How to find the slope and y-intercept of a table? ›

Take the equation y = mx + b and plug in the m value (m = 1) and a pair of (x, y) coordinates from the table, such as (2, 43). Then solve for b. Finally, use the m and b values you found (m = 1 and b = 41) to write the equation. Now check your answer.

Top Articles
Latest Posts
Article information

Author: Tish Haag

Last Updated:

Views: 5279

Rating: 4.7 / 5 (67 voted)

Reviews: 90% of readers found this page helpful

Author information

Name: Tish Haag

Birthday: 1999-11-18

Address: 30256 Tara Expressway, Kutchburgh, VT 92892-0078

Phone: +4215847628708

Job: Internal Consulting Engineer

Hobby: Roller skating, Roller skating, Kayaking, Flying, Graffiti, Ghost hunting, scrapbook

Introduction: My name is Tish Haag, I am a excited, delightful, curious, beautiful, agreeable, enchanting, fancy person who loves writing and wants to share my knowledge and understanding with you.